The time-dependent analysis of prestressed concrete bridges built adopting the incremental launching technique is presented. After summarizing the well known results derived from the elastic analysis, the problem is approached in the visco-elastic domain taking into account the effects consequent to the complex load history affecting the structure. In particular, the effects produced by prestressing applied both in the launching phase and after it and by application of imposed displacements and of delayed restraints during the launching phases are carefully investigated through a refined analytical procedure. The reliability of the proposed algorithm is tested by means of comparisons with reference cases for which exact solutions are known. A case study of general interest is then discussed in detail. This case study demonstrates that a purely elastic approach represents a too crude approximation, which is unable to describe the specific character of the problem.